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Journal of Physics B Atomic and Molecular Physics

Non-Lorentzian laser lineshapes in intense field-atom interaction

P. Zoller, P. Lambropoulos

Published Sep 28, 1979• 86 citations
Publisher

Abstract

The effect of a cut off of the Lorentzian laser lineshape (as predicted by the phase-diffusion model of ideal laser theory) on the laser-atom interaction is investigated. The damping terms in the averaged density matrix equation of the atom, arising from the finite laser bandwidth are shown to be multiplied by a detuning-dependent cut-off. For detunings of the laser well within the Lorentzian part of the spectrum, the authors recover the previously derived results, while these damping terms are seen to drop out for detuning larger than the cut-off. Within their model, therefore, a laser with a lineshape falling faster than a Lorentzian, and for large detunings, appears monochromatic to the atom. In particular, the authors obtain qualitative agreement with recent experiments in which the reversed peak asymmetry in the doublet of double optical resonance persists only within a certain range of detuning from resonance.

DOI
10.1088/0022-3700/12/18/003

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Physical Review A•May 1, 1981•42 citations
The effect of a cut off of the Lorentzian laser lineshape (as predicted by the phase-diffusion model of ideal laser theory) on the laser-atom interaction is investigated. The damping terms in the averaged density matrix equation of the atom, arising from the finite laser bandwidth are shown to be multiplied by a detuning-dependent cut-off. For detunings of the laser well within the Lorentzian part of the spectrum, the authors recover the previously derived results, while these damping terms are seen to drop out for detuning larger than the cut-off. Within their model, therefore, a laser with a lineshape falling faster than a Lorentzian, and for large detunings, appears monochromatic to the atom. In particular, the authors obtain qualitative agreement with recent experiments in which the reversed peak asymmetry in the doublet of double optical resonance persists only within a certain range of detuning from resonance.
The interaction of an atomic system with a laser having phase fluctuations is studied within the phase-diffusion model, with the finite correlation time of the time derivative of the phase taken into account. This finite correlation time introduces a line shape which is Lorentzian near the center and falls off faster than the Lorentzian at its wings. The authors apply this model to calculate the spectrum of double optical resonance for excitation by a laser having this non-Lorentzian line shape. It is observed that the reversed peak asymmetry reverts to normal far off resonance owing to the cutoff of the laser spectrum, in agreement with recent experiments. Numerical results are presented.
According to laser theory the lineshape of a laser broadened by Ornstein-Uhlenbeck phase fluctuations is non-Lorentzian. The equations describing the interaction of such a laser with atomic systems are cast into a form which has the same structure as the density-matrix equations in the absence of fluctuations but with modified detunings, damping parameters and interaction matrix elements. By these means the authors derive substitution rules for taking into account the effect of these non-Lorentzian lineshapes which generalize those already known for Lorentzian lineshapes arising from Wiener-Levy fluctuations. The theory is applied to two-photon ionisation and analytic expressions are obtained for the rate of this process. For the extended two-level model the authors' results agree with those of Yeh and Eberly (1981) in the appropriate limit, but they also consider a more general model which leads to enhanced single-photon ionisation rates.
The authors examine the theory of optical double resonance using two lasers whose finite linewidths are produced by the process of phase-diffusion. Their lineshapes, which are nonLorentzian, are characterised by a bandwidth B and a cut off C. The authors are concerned with obtaining an analytic theory; they achieve this by assuming the ratio B/C to be small and work to first order in B/C (although the method can be extended to higher order in B/C). They obtain analytic expressions for the optical double resonance spectrum and discuss the results of recent experiments by Hogan et al. (1978) and Nitz et al. (1981) in which it was found that the asymmetry of the peaks in the optical double resonance spectrum changed with detuning. It is found that a qualitative understanding can be achieved but that a full quantitative comparison is not yet possible.
Lorentzian models for laser line shapes lead to qualitatively incorrect results for off-resonance excitation of atoms. This paper is the first attempt to present a theory of the nonperturbative interaction of an atom with a chaotic field (representing multimode laser radiation having strong amplitude fluctuations) with a line shape falling off faster than a Lorentzian. To this end we suggest a stochastic Markovian model for a non-Lorentzian chaotic field. To solve the multiplicative stochastic differential equations describing the atom-field interaction we propose a "marginal characteristic function approach." This not only reproduces our earlier results in a more elegant way and establishes the relationship between approaches used by other authors in a different context, but also provides the simplest possible basis for our present discussion of ac Stark splitting in double optical resonance. While for a chaotic field with a Lorentzian line shape the asymmetry of the two-peaked off-resonance spectrum is reversed for all values of the detuning compared with the monochromatic case, our present model predicts a reversed peak asymmetry only for detunings smaller than a few laser bandwidths in agreement with experiment. The on-resonance spectrum is dominated by the amplitude fluctuations and is only weakly affected by changes of the spectral line shape of the laser.
Cross correlation refers to the situation in which the fluctuations in the fields of two or more lasers are correlated in some way. Recently, Thomas et al. [ Opt. Lett.6, 298 ( 1981); Phys. Rev. Lett.48, 867 ( 1982)] proposed the generation of cross correlation between two laser fields interacting with a three-level system as a means of reducing noise and went on to exploit this property in the observation of narrow Ramsay fringes. Dalton and Knight [ J. Phy. B15, 3997 ( 1982)] discussed the theoretical aspects of cross correlation and showed that it produced interesting effects in population trapping for example. We have demonstrated that it has significant effects on the optical double-resonance (ODR) spectra [ J. Phys. B17, L389 ( 1984)]. On the other hand, the effects of non-Lorentzian laser line shapes have been shown by various workers to have significant effects on a wide range of phenomena, such as multiphoton ionization, resonance fluorescence, and ODR. In this paper we present a theory of the interactions of lasers whose fluctuations are governed by the phase-diffusion process with atomic systems that includes the effects of cross correlation and non-Lorentzian line shapes. We derive the basic equations (which in general have to be solved numerically) and obtain analytic results in the case in which the line shape is approximately Lorentzian near line center but falls off faster than a Lorentzian in the wings. We believe that this analytic model shows all the essential features of the interplay between cross correlation and non-Lorentzian line shapes. The theory is applied to the ODR experiment. In particular, we find that the asymmetry of the spectra is strongly affected by these two features, and so is the ODR spectral line shape when the saturating laser intensity is close to the threshold for producing two peaks.
The effects of different laser line shapes on the intensity and spectrum of resonance fluorescence from a two-level atom are investigated. The laser model considered is that of an ideal single-mode laser operating high above threshold, with constant amplitude and undergoing phase-frequency fluctuations analogous to Brownian motion. As the correlation time of the frequency fluctuations increases from zero to infinity, the laser line shape changes from Lorentzian to Gaussian in a continuous way. It is shown that for intermediate and strong fields, the average intensity of fluorescence in the case of a resonant broadband Lorentzian line shape is higher than that in the case of a Gaussian line shape with the same bandwidth and total power. This is in contrast to the weak-field case where the higher peak power of the Gaussian line shape makes it more effective than the Lorentzian line shape. It is also shown that in the case of a nonzero frequency correlation time (non-Lorentzian line shape) the intensity of fluorescence undergoes non-Markovian fluctuations. In relation to the spectrum of resonance fluorescence, it is shown that as the line shape is varied from Lorentzian to Gaussian the following changes take place: In the case of off-resonance excitation, the asymmetry of the spectrum decreases. In the case of resonant excitation, the center-peak to side-peak height ratio for the triplet structure increases. Moreover, the recently predicted center-line dip, which develops in the spectrum in the case of broadband excitation when the Rabi frequency and the bandwidth are nearly equal, becomes increasingly deeper.